Question

in the right triangle shown below, what is the length of the missing side length labeled x? 13 14 15 16

Explanation:

Step1: Apply Pythagorean theorem

For a right - triangle, \(a^{2}+b^{2}=c^{2}\), where \(c\) is the hypotenuse. Here \(a = 12\), \(b = 5\), and \(c=x\).
So, \(x^{2}=12^{2}+5^{2}\).

Step2: Calculate \(12^{2}\) and \(5^{2}\)

\(12^{2}=144\), \(5^{2}=25\). Then \(x^{2}=144 + 25\).

Step3: Sum the values

\(x^{2}=169\).

Step4: Take the square root

\(x=\sqrt{169}\), since \(x>0\) (length of a side), \(x = 13\).

Answer:

13